D.C. Corporation Counsel John R. Risher Jr.'s effort to remove Sterling Tucker as City Council chairman comes at a time when one confidential political poll has indicated that Tucker would be a 2-to-1 winner over Risher's boss, Mayor Walter E. Washington, in a race for mayor.

Sources who have seen the results of the poll, said to have been taken within the past several weeks by a professional polling organization, say it is one of the most recent indicators of the mayor's slumping political stock and the threat posed by Tucker.

In a three-way race with Tucker and the other major mayoral hopeful, Council member Marion Barry (D-at large), Washington would finish well behind Tucker, the poll is said to indicate. Tucker would beat both men by 3-to-2 margins, based on current attitudes, according to those who have seen the poll.

The City Council chairman would be the victor in seven of the city's eight wards. The other ward - ward six in the Capitol Hill area - would probably be taken by Barry, according to those who have seen the poll.

The findings of the poll have added to the atmosphere of political maneuvering that accompanied Risher's filling Monday in Superior Court of a petition asking that Tucker be removed as City Council chairman for allegedly violating city restrictions on outside employment.

For the past two years, Tucker has been an adjunct associate professor at Howard University and received a salary of about $7,500 per ytar. The city's home rule charter requires the chairman to work full-time for the city and not hold any other job.

As compensation, the chairman is paid $35,000 a year - $10,000 more than the other 12 members of the Council, who are allowed to have outside employment.

Tucker has maintained that at the time the home rule legislation was being framed, he informed key congressional leaders of his employment at Howard and was told it was not barred by the legislation. In addition, he has routinely reported his income from the lecturing job in annual public reports to the D.C. Board of Elections and Ethics.

Risher maintained in the petition that by holding the lecturing job Tucker had "forfeited" his right to hold office. Citing a little-known section of the D.C. Code governing violations of the public trust, Risher asked the court to declare the Council chairmenship vacant.

Yesterday, Chief Judge Harold H. Greene said that, at the request of both sides, he would personally preside over the proceedings, which could include a jury trial if Tucker's lawyers request one.

Risher, the city's chief lawyer and a close political confidant of the mayor, began an investigation of the Tucker situation three weeks ago. Three days before the petition was filed, Risher insisted in an interview that he was merely carrying out the duties of his office and not doing the mayor's biding" by investigating a possible political foe of Washington.

Yesterday, Risher refused to answer any questions about his knowledge of the poll at the time of the investigation. Mayor Washington, who has insisted repeatedly that he had no prior knowledge of Risher's action, said through a spokesman that he too was unaware of any such poll.

Tucker campaigned with the mayor in 1974. Since that time, however, the former civil rights leader has become what many city political observers believe the biggest threat to the mayor's political future.

Washington is 62, Tucker is 53 and both have a history of being political moderates. Both have strong ties to influential city businessman and middle-class blacks and whites.

Barry, on the other hand is younger (41) and has a background in black comminity organizing, with less support among businessmen who still remember his days of street corner activism.

Some observers believe that in a three-way race, Tucker would take more votes from the mayor than Barry. With Tucker out of the race, Tucker's supporters would be more likely to bote for and contribute to Washington than to Barry.

Privately, many close supporters of the mayor have complained that Tucker has received less extensive press coverage in cases where he has been accused of questionable action.

The mayor, on the other hand, had to contend with weeks of front page stories critical of the administration of the troubled Department of Human Resources, which had been headed by Joseph P. Yeldell, the mayor's long time friend and political ally.